MCQ
$\frac{\sin 3 A-\cos \left(\frac{\pi}{2}-A\right)}{\cos A+\cos (\pi+3 A)}=$
- Atan A
- Bcot A
- Ctan 2A
- ✓cot 2A
✓
Answer
Correct option: D.
cot 2A
(D)
$\frac{\sin 3 A-\cos \left(\frac{\pi}{2}-A\right)}{\cos A+\cos (\pi+3 A)}=\frac{\sin 3 A-\sin A}{\cos A - \cos 3 A}$
$=\frac{2 \cos 2 A \sin A }{2 \sin 2 A \sin A }$
$= cot 2A$
$\frac{\sin 3 A-\cos \left(\frac{\pi}{2}-A\right)}{\cos A+\cos (\pi+3 A)}=\frac{\sin 3 A-\sin A}{\cos A - \cos 3 A}$
$=\frac{2 \cos 2 A \sin A }{2 \sin 2 A \sin A }$
$= cot 2A$
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